I wouldnt cut it only cause it still is in good condition but i think creating more air flow is always a good thing so maybe get an old bar to hack up and paint it but it depends if you really care much about destroying a good bar....

Or go find a aero front bar that will give you more flow and improve the look IMO

Yeah if u cut it - you car will attract more attention due to the fact that more intercooler is showing.

Yes, it will help airflow - but the worst part is the pipe to the TB - that gets the hottest.
The cooler is cool no matter what. Unless its like 36 degrees, but if the car is being driven, air is flowing through.

Yea the bottom of the bar actually helps with aerodynamics. If you cut out the bottom you'll get worse airflow like Hawker180 said above.
That and it looks like aids without the bottom.. I say if you're going to cut it just cut the middle beam out and fibreglass it flat over the cuts.